Hybrid ferromagnetic/piezoelectric core-shell nanoparticles and ceramics have potential for a wide range of applications due to their tunability, electronic and magnetic properties. In this study, we designed a core-shell-type nanostructure of composition CoFe2O4/BNT-BT0.08, where BNT-BT0.08 is the abbreviation of bismuth, sodium titanate (Bi0.5Na0.5TiO3, BNT) doped with 8 mol% barium titanate (BaTiO3, BT). This multiferroic composite was prepared by covering CoFe2O4 nanoparticles with a shell of BNT-BT0.08 using the sol-gel technique. Scanning and transmission electron microscopy confirmed formation of a core-shell structure. The results of microstructure, dielectric, piezoelectric and magnetic investigations demonstrated that this heterostructure shows simultaneously electrical and magnetic behavior, at room temperature. XRD pattern of core-shell composite CoFe2O4/BNT-BT0.08 powder reveals only cubic CoFe2O4 and rhombohedral Bi0.5Na0.5TiO3 phases. CoFe2O4/BNT-BT0.08 core-shell nanostructure sample shows high values of permittivity (epsilon >= 600) together with high dielectric losses (tan delta >= 1) in the low-frequency range (nu <= 10(4) Hz). PFM and polarization hysteresis indicated a ferroelectric domains structure and remnant polarization of similar to 2.6 A mu C/cm(2) for the ceramics pellets samples of CoFe2O4/BNT-BT0.08. The present study reveals the possibility of coating nanoparticles onto nanometer-sized core particles, using controlled sol-gel process, in order to prepare multifunctional core-shell composites for piezoelectric and magnetoelectronic sensors.